Evaluate
\frac{114}{25}=4.56
Factor
\frac{2 \cdot 3 \cdot 19}{5 ^ {2}} = 4\frac{14}{25} = 4.56
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)456}\\\end{array}
Use the 1^{st} digit 4 from dividend 456
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)456}\\\end{array}
Since 4 is less than 100, use the next digit 5 from dividend 456 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)456}\\\end{array}
Use the 2^{nd} digit 5 from dividend 456
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)456}\\\end{array}
Since 45 is less than 100, use the next digit 6 from dividend 456 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)456}\\\end{array}
Use the 3^{rd} digit 6 from dividend 456
\begin{array}{l}\phantom{100)}004\phantom{6}\\100\overline{)456}\\\phantom{100)}\underline{\phantom{}400\phantom{}}\\\phantom{100)9}56\\\end{array}
Find closest multiple of 100 to 456. We see that 4 \times 100 = 400 is the nearest. Now subtract 400 from 456 to get reminder 56. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }56
Since 56 is less than 100, stop the division. The reminder is 56. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}